A paper on the new model is published early
online in the Swedish journal Tellus A. The paper
is called “A Thermodynamically General Theory for
Convective Vortices.” It is available at:
<http://www3.interscience.wiley.com/journal/119879028/abstract>

ANN ARBOR, Mich.—A new mathematical model
indicates that dust devils, water spouts,
tornadoes, hurricanes and cyclones are all born
of the same mechanism and will intensify as
climate change warms the Earth’s surface.

The new equation, developed by University of
Michigan atmospheric and planetary scientist
Nilton Renno, could allow scientists to more
accurately calculate the maximum expected
intensity of a spiraling storm based on the depth
of the troposphere and the temperature and
humidity of the air in the storm’s path. The
troposphere is the lowest layer of Earth’s
atmosphere.

This equation improves upon current methods,
Renno says, because it takes into account the
energy feeding the storm system and the full
measure of friction slowing it down. Current
thermodynamic models make assumptions about these
variables, rather than include actual quantities.

“This model allows us to relate changes in
storms’ intensity to environmental conditions,”
Renno said. “It shows us that climate change
could lead to increases in how efficient
convective vortices are and how much energy they
transform into wind. Fueled by warmer and moister
air, there will be stronger and deeper storms in
the future that reach higher into the atmosphere.”

Renno and research scientist Natalia Andronova
used the model to quantify how intense they
expect storms to get based on current climate
predictions. For every 3.6 degrees Fahrenheit
that the Earth’s surface temperature warms, the
intensity of storms could increase by at least a
few percent, the scientists say. For an intense
storm, that could translate into a 10 percent
increase in destructive power.

Renno’s model is what scientists call a
“generalization” of Daniel Bernoulli’s
18th-century equation that explains how airplane
flight is possible. Bernoulli’s equation
basically says that as wind speed increases, air
pressure decreases. It leaves out variables that
were considered difficult to deal with such as
friction and energy sources (which, in the case
of a whirling storm, is warm air and condensation
of water vapor.) And in certain idealized
situations, omitting that information works fine.

But by including these additional variables,
Renno was able to broaden Bernoulli’s equation to
apply it to more general phenomena such as
atmospheric vortices.

“The laws of physics are generally very simple,”
Renno said. “When you make assumptions, you are
not representing the simple, basic law anymore.
If you don’t make assumptions, your equations
have those simple, basic laws in them. It gets a
little more complicated to get to the solution,
but you don’t introduce error, and you answer is
more elegant, more simple.”

Renno’s work bolsters studies by others who say
hurricanes have grown stronger over the past 50
years as sea surface temperatures have risen.
This effect has not been extreme enough for
humans to notice without looking, scientists say.
Hurricane Katrina and Cyclone Nargis were not the
most intense storm to hit land in the past half
century. Other factors contributed to the
devastation they caused.

This new model helps explain the formation of
spiral bands and wall clouds, the first clouds
that descend during a tornado. It’s clear now
that they are the result of a pressure drop where
the airspeed has increased.

“This is the first thermodynamic model that
unifies all these vortices,” he said. “When you
unify them, you can see the big picture and you
can really understand what makes them form and
change.”

A co-investigator on NASA’s Mars Phoenix Lander
mission, Renno has used his new model to
calculate the intensity of dust storms in Mars’
polar regions. He found that at the Phoenix
landing site dust storms can have winds in excess
of 200 mph.

###

Renno is an associate professor in the Department
of Atmospheric, Oceanic and Space Sciences.
Andronova is a research scientist in the
Department of Atmospheric, Oceanic and Space
Sciences.

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